You can use whomever you like for your fulfillment/shipping, regardless of which plan you are on with Shopify.
However, if you are looking to have your rates from Stamps.com shown at checkout to your customers, you will have to enable the real-time carrier-calculated rates at checkout. In order to do this, you will have to choose one of three options:
If you are only using USPS from Stamps.com, however, you may want to just compare the rates that Shopify Shipping quotes to the same shipments from Stamps.com and skip the above step if it isn't needed. In my experience, the USPS commercial rates from Stamps and Shopify have been the same, so you may not need to show your Stamps.com rates at checkout, as you can just show the Shopify USPS rates since they're the same.